Aircraft: EMB ERJ 170/175 ER/LR
Phase of flight: Parked
Anomaly: Deviation / Discrepancy - Procedural Hazardous Material Violation; Deviation / Discrepancy - Procedural Published Material / Policy

After sorting out an issue in ZZZ of not getting a cargo load report (CLR) notes on ACARS on any live animals. The flight crew simply asked [the] ramp agents to resend it. They were unable to do so so we simply asked for a paper CLR. The Ramp Lead became flustered with his scanner and went to go ask a manager for help. The manager came back about 10 minutes later after we had closed and gave the flight crew the notice to Captain form (first time we discovered there was dangerous goods onboard) and resent the CLR with the notes on DG (Dangerous Goods) and live animal (I noticed the bird and medical boxes on my walk around but didn't notice any markings on the medical boxes pertaining to DG). Already delayed pushing back we then became saturated with a runway change. Reaching cruise we became talking more about the lack of NOTOC (Notice to Captain) and an impending incident report. After talking for a few moments at cruise. I realized that we are not allowed to be carrying both dry ice and any live animals in the forward cargo bin together. After bringing that to light I began inquiring about possible diversion options. Including the destination of ZZZ1 40-45 minutes out. After the Captain messaged with Dispatch we decided to divert to ZZZ2 as that was the fastest option to separate the dry ice and live animal. Landing and taxing in we made sure we had a ramp crew that was informed of the situation and needing to open the fwd cargo door asap and remove the live animal. As well as a gate in ZZZ2. I went down to check as soon as the jet bridge was pulled up. And when I got down there the bird was out of the fwd cargo and in good health. The live bird was ok and the ramp agents took the bird into the office to be in the air conditioning and off the loud ramp environment while the ramp crew and flight crew figured out a new bag count. Cargo count. And any other required paperwork. I began calling for fuel. Loading in the new flight plan from the release while the Captain went down to talk to ramp managers as to what cargo is staying or going. A new and confirmed bag count after ZZZ2 rampers recounted bags and cargo (which did not match the original bag count out of ZZZ even though we only removed the DG) was received.After getting everything all figured out in ZZZ2 we calmly talked to the passengers and gave them a timeline of when we would expect to be pushing back and going to ZZZ1. After getting to ZZZ1. And finishing the flight. Deplaning. And; making sure the live animal was ok and in the possession of ZZZ1 Ramp Operations. The Captain and I began debriefing today's events. We reconstructed a timeline. No cargo load remarks. Called OPS. They began to get flustered about their system. We then just asked for a paper cargo load report to remedy the glitch in the system. The Ramp Manager came and threw though the window a notice to Captain. This was the very first time we realized we had any DG onboard. We then hyper focused on the problem of closing without a NOTOC and making sure to talk to OPS and Ground. When talking about this in the air. I realized the problem of the DG and live animal in the same compartment. We quickly then realized that this was not a situation that could continue. We began looking at diversion options. Talking to Dispatch and ZZZ2 OPS. We diverted and handled the situation at hand going forward. We talked about how there are numerous safeguards to never let a situation like this happen before it even gets to the airplane or airport/cargo processing counter for that matter. And how this is a prime example of reasons [for the] swiss cheese model. Starting early this morning with 3 runway changes and a wrong turn on a taxiway resulting in the first ASAP. Airline's ramp scanning system and software letting these be scanned together or a safeguard overridden to let this happen. Us hyperfocusing on discovering DG was onboard after closing with no NOTOC. And resulting in missing the combined DG and live animal in the same cargo compartment until cruise flight. Going forward and learning from this. This is a prime example of how to simply complete tasks and move on without hyperfocusing on the previous threats or errors. Today I; while operating Aircraft X from ZZZ-ZZZ1; made a grave mistake and allowed myself to depart ZZZ with dry ice and a parrot in the forward cargo bin. Upon discovering my mistake I contacted Dispatch and subsequently diverted to ZZZ2. The parrot was alive and we got some gas and continued onto ZZZ1 without further incident. While in ZZZ my FO (First Officer) noticed a big parrot and some medical looking boxes sitting outside cargo bin during preflight. He brought it to my attention. I was focused on making sure we had one or the other listed on load remarks. We got our baggage data but it did not generate a load remarks message. I released parking break while talking to [the] Ramp Lead via interphone. I inquired as to why we did not have a load remarks message. I asked if he could resend it. He was unsure of everything and went to find his supervisor. At this time I could not confirm if we had an animal or DG or both. I called Dispatch to see if he could look at stuff for me and he confirmed we got bag total the weight of some cargo thru close out but no load remarks. As a side bar I spoke with Name1 on the Hazmat hotline and he stated that company had to manually override scanner to allow for DG and animal at same time. Could this be why we didn't get load remarks? After about 10 minutes; [a] ramp agent returned but paced. He did not get back on intercom during most of this but when he did I explained he had a couple options. We could do a return to gate or they could give me a paper CLR (Cargo Load Report) thru [the] window if they could not fix it with [the] scanner. He radioed someone and a minute or so later a supervisor came out of an office and did not look happy. He had a wad of paper. He came to FO side and tossed the wad of paper thru window which ended up being the NOTOC for the dry ice. At about the same time we received the load remarks and I was focused on the DG the live animal got past me. I did not do this on purpose. At the time I was more upset with blocking out without the knowledge of DG on board and focused on making sure I had all my correct paperwork and it matched since I had DG. We also had the remark 'EXST:9A'. This threw me for a loop because I didn't know what it meant. We figured it out to be that a passenger had bought a seat onboard a raft for an animal which I already knew about because of gate agents and flight attendants. We had wasted enough time so I decided to continue with the push. We had a runway change on taxi out so I focused on getting thru that and we as a crew focused on operating safely until we were in a low workload environment to talk about it again. At cruise I was filling out incident report for not getting NOTOC when I was talking my narrative out loud the FO was looking at [the] FOM and said we have both an animal and DG on board and he just realized it as he was reading and telling me. We immediately contacted Dispatch who advised us to go to ZZZ2 or ZZZ3 and divert. I chose ZZZ2. I alerted [the] flight attendants and we landed in ZZZ2 without further incident. There was confusion on [the] ground in ZZZ2 as to which item should continue with us. The bird or dry ice. I called Dispatch again and they chose the dry ice and while I was talking to ramp they said company wanted to keep bird to ZZZ1. While checking packages manually in cargo bin I discovered the DG also contained Blood. UN3373. After OPS and company agreed; we departed to ZZZ1 without further incident. After landing I called Hazmat hotline and submitted pictures of bird and DG and ACARS remarks to company.I did not purposefully depart without NOTOC or depart consciously knowing we had dry ice and a bird in same bin. I know it's one or the other. I was just hyper focused on being legal that I missed connecting the two together. I believe I realize now that I can take as much time as I need to make good decisions. No need to rush. I did and it got me nowhere. I hope someone can imagine getting a wadof paper thrown into flight deck and the distractions of finally realizing the gravity of I had almost departed without knowing what was in cargo bin. I had always believed there were safeguards in place to prevent this from happening. This is the first time in 15 years of safe flying I've had to divert for a bad decision I made. I feel horrible and I'm glad the animal was still alive. I know it could have been much worse. I believe this flight had a happy outcome because of Dispatch and my crew. I tried to thank them but I cannot thank them enough. E-175 flight crew reported an uneventful diversion due to Hazmat loading issue due to missing NOTOC at departure.